Suppose a rocket ship in deep space moves with constant acceleration equal to 9.8 m/s2, which gives the illusion of normal gravity during the flight. (a) If it starts from rest, how long will it take to acquire a speed one-tenth that of light, which travels at 3.0 * 108 m/s? (b) How far will it travel in so doing?

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Physics

Dylan Stanley

Today, 12:44

Suppose a rocket ship in deep space moves with constant acceleration equal to 9.8 m/s2, which gives the illusion of normal gravity during the flight. (a) If it starts from rest, how long will it take to acquire a speed one-tenth that of light, which travels at 3.0 * 108 m/s? (b) How far will it travel in so doing?

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Ayana Miranda · Answer 1

(a).

It starts from rest, and its speed increases by 9.8 m/s every second.

One tenth the speed of light is (1/10) (3 x 10⁸ m/s) = 3 x 10⁷ m/s.

To reach that speed takes (3 x 10⁷ m/s) / (9.8 m/s²) = 3,061,224 seconds.

That's about 35 days and 10 hours.

(b).

Distance traveled = (average speed) x (time of travel)

Average speed = (1/2) of (1/10 the speed of light) = 1.5 x 10⁷ m/s.

Time of travel is the answer to part (a) above.

Distance traveled = (1.5 x 10⁷ m/s) x (3,061,224 sec) = 4.59 x 10¹³ meters

That's 45.9 billion kilometers.

That's 28.5 billion miles.

That's about 6.2 times the farthest distance that Pluto ever gets from the Sun.